You are given two non-negative integers (a, b). You can apply two types of operations on (a) any number of times and in any order: (a \gets a + 1). The cost of this operation is (x); (a \gets a \oplus 1), where (\oplus) denotes the bitwise XOR operation . The cost of this operation is (y). Now you are asked to make (a = b). If it's possible, output the minimum cost; otherwise, report it. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The only line of each test case contains four integers (a, b, x, y) ((1 \le a, b \le 100, 1 \le x, y \le 10^7)) — the two integers given to you and the respective costs of two types of operations. For each test case, output an integer — the minimum cost to make (a = b), or (-1) if it is impossible. In the first test case, the optimal strategy is to apply (a \gets a + 1) three times. The total cost is (1+1+1=3). In the second test case, the optimal strategy is to apply (a \gets a + 1), (a \gets a \oplus 1), (a \gets a + 1), (a \gets a \oplus 1) in order. The total cost is (2+1+2+1=6). In the fifth test case, it can be proved that there isn't a way to make (a = b).